6 papers · 1 filter
On I-eigenvalue free threshold graphs
Luiz Emilio Allem, Elismar R. Oliveira, Fernando Tura
A graph is said to be I-eigenvalue free if it has no eigenvalues in the interval I with respect to the adjacency matrix A. In this paper we present two algorithms for generating I-…
Null Decomposition of Unicyclic Graphs
Luiz Emilio Allem, Daniel Alejandro Jaume, Gonzalo Molina +2
In this work we obtain basis for the null space of unicyclic graphs. We extend the null decomposition of trees from [11] for unicyclic graphs. As an application, we obtain closed f…
Independence and Matching Numbers of Unicyclic Graphs From Null Space
Luiz Emilio Allem, Daniel Alejandro Jaume, Gonzalo Molina +2
We characterize unicyclic graphs that are singular using the support of the null space of their pendant trees. From this, we obtain closed formulas for the independence and matchin…
Integral cographs and applications
Luiz Emilio Allem, Fernando Tura
A graph is called integral if all the eigenvalues of its adjacency matrix are integers. In this paper, we show a cograph that has a balanced cotree $T_{G}(a_{1},\ldots,a_{r-1},0|0,…
Short note on Randić energy
Luiz Emilio Allem, Gonzalo Molina, Adrián Pastine
In this paper, we consider the Randić energy of simple connected graphs. We provide upper bounds for in terms of the number of vertices and the nullity of the graph. We p…
Multiplicity of eigenvalues of cographs
Luiz Emilio Allem, Fernando Tura
Motivated by the linear time algorithm that locates the eigenvalues of a cograph G [10], we investigate the multiplicity of eigenvalue for λ\neq -1,0. For cographs with balanced co…